# Obtaining prizes - Need help creating a simulation

• Oct 1st 2012, 11:24 AM
jthomp18
Obtaining prizes - Need help creating a simulation
Each box of (brand) cereal contains 1 of 5 different prizes. If there is an equal chance of obtaining each prize, then how many boxes of cereal would you need to purchase in order to collect all of the prizes? Design a simulation that will approximate this result. Explain your experimental design and results.

Can someone help me? I do not know where to begin.
• Oct 1st 2012, 01:05 PM
ebaines
Re: Obtaining prizes - Need help creating a simulation
If you want to be guarranteed to have at least one of each prize it requires an infinite number of boxes. Here's why: suppose that after collecting 4 boxes you happen to have gotten 4 different prizes - let's call them A, B, C and D - and so the only one missing is prize E. On the fifth box there's a 1 in 5 chance that it contains a prize E, so 4 out of 5 times you'll have to buy another box. But when you buy the 6th box there's only a 4/5 change it has prize E, so you are likely to have to continue on. As you buy more boxes the probability of not ever getting prize E gets smaller, but it never goes to zero.

For a simulation you can use a random number genarator that determines whether prize 1, 2, 3, 4, or 5 comes in each box, and run a Monte Carlo simulation to see the number required to get at keast one of each prize. You will probably find that it typically takes about 10, with as few as 5 and occasionally needing as many as 20 or more.
• Oct 3rd 2012, 03:43 PM
jthomp18
Re: Obtaining prizes - Need help creating a simulation